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The multivariate Faà di Bruno formula and multivariate Taylor expansions with explicit integral remainder term

  • Roy B. Leipnik and Charles E. M. Pearce

Abstract

The Faà di Bruno formulæ for higher-order derivatives of a composite function are important in analysis for a variety of applications. There is a substantial literature on the univariate case, but despite significant applications the multivariate case has until recently received limited study. We present a succinct result which is a natural generalization of the univariate version. The derivation makes use of an explicit integralform of the remainder term for multivariate Taylor expansions.

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References

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The multivariate Faà di Bruno formula and multivariate Taylor expansions with explicit integral remainder term

  • Roy B. Leipnik and Charles E. M. Pearce

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